Three dimensional printing material system and method using plasticizer-assisted sintering

ABSTRACT

Materials system, kit, and methods are provided to enable the formation of articles by three dimensional printing. The kit includes (i) a substantially dry particulate material including an aqueous-insoluble thermoplastic particulate material, plaster, and a water-soluble adhesive; (ii) an aqueous fluid binder, and (iii) an infiltrant.

RELATED APPLICATIONS

This application claims priority to and is a divisional of U.S. patentapplication Ser. No. 12/035,743, filed Feb. 22, 2008, which claims thebenefit of U.S. Provisional Patent Application Ser. No. 60/902,782,filed Feb. 22, 2007; the disclosures of both applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

This invention relates generally to rapid prototyping techniques and,more particularly, to a three-dimensional printing material and methodusing plasticizer-assisted sintering.

BACKGROUND

The field of rapid prototyping involves the production of prototypearticles and small quantities of functional parts, as well as structuralceramics and ceramic shell molds for metal casting, directly fromcomputer-generated design data.

Two well-known methods for rapid prototyping include a selective lasersintering process and a liquid binder three dimensional printingprocess. These techniques are similar, to the extent that they both uselayering techniques to build three-dimensional articles. Both methodsform successive thin cross-sections of the desired article. Theindividual cross-sections are formed by bonding together adjacent grainsof a granular, i.e. particulate material on a generally planar surfaceof a bed of the granular material. Each layer is bonded to a previouslyformed layer to form the desired three-dimensional article at the sametime as the grains of each layer are bonded together. Thelaser-sintering and liquid binder techniques are advantageous, becausethey create parts directly from computer-generated design data and canproduce parts having complex geometries. Moreover, three dimensionalprinting can be quicker and less expensive than machining of prototypeparts or production of cast or molded parts by conventional “hard” or“soft” tooling techniques, that can take from a few weeks to severalmonths, depending on the complexity of the item.

An early three dimensional printing technique, described in U.S. Pat.No. 5,204,055, incorporated herein by reference in its entirety,describes the use of an ink-jet style printing head to deliver a liquidor colloidal binder material to sequentially applied layers of powderedmaterial. The three-dimensional ink-jet printing technique or liquidbinder method involves applying a layer of a powdered material to asurface using a counter-roller. After the powdered material is appliedto the surface, the ink-jet printhead delivers a liquid binder in apredetermined pattern to the layer of powder. The binder infiltratesinto gaps in the powder material and hardens to bond the powder materialinto a solidified layer. The hardened binder also bonds each layer tothe previous layer. After the first cross-sectional portion is formed,the previous steps are repeated, building successive cross-sectionalportions until the final article is formed. Optionally, an adhesive canbe suspended in a carrier that evaporates, leaving the hardened adhesivebehind. The powdered material may be ceramic, metal, plastic or acomposite material, and may also include fibers. The liquid bindermaterial may be organic or inorganic. Typical organic binder materialsused are polymeric resins or ceramic precursors, such aspolycarbosilazane. Inorganic binders are used where the binder isincorporated into the final articles; silica is typically used in suchan application.

As described in U.S. Pat. No. 6.007,318, incorporated herein byreference in its entirety, printed articles may be dipped or paintedwith a solution that infiltrates the article by capillary actions. Thisprocessing may improve handling properties of the article and preventits decay.

The use of an absorbent filler to facilitate infiltrant absorption isdescribed in U.S. Patent Application 2005/0059757, incorporated hereinby reference in its entirety. That application describes theincorporation of thermoplastic fillers in a powder, with the activatingor infiltration material being a solvent.

SUMMARY

In an embodiment, a strong printed article may be made by threedimensional printing over a substantially dry particulate material buildmaterial including an aqueous-insoluble thermoplastic particulatematerial. The printed article is further post-processed by infiltratinga liquid medium into the article. The liquid medium selectivelyplasticizes the aqueous-insoluble thermoplastic particulate material,lowering the thermoplastic's glass transition temperature. Thisfacilitates sintering of the thermoplastic particulate material to bondtogether the matrix of the article, thereby increasing the article'sdurability.

Typical existing printing processes include a post-processinginfiltration step to increase the strength of the printed article usingtwo-component casting resins and/or adhesives or one-componentcyanoacrylate adhesives to achieve greater durability to athree-dimensional article. Articles printed with the particulatematerial build material described herein and further infiltrated with aliquid plasticizer have strengths comparable to that of articles formedwith cyanoacrylate adhesive, e.g., about 20 MPa, which has historicallybeen proven to be sufficient for most concept modeling applications.

The infiltrant materials used for plasticized sintering may provide someadvantages over other build materials. Using two-component castingresins such as epoxy-amine, isocyanate-amines, and/or isocyanate-polyolsystems decreases the ease-of-use by the end-user by incorporating extramixing steps, imposing pot-life constraints, and giving rise to safety,health, and environmental issues. One-component cyanoacrylate adhesivestypically offer better ease-of-use because these materials do notrequire mixing, but they may create safety, heath, and environmentissues such as fumes, irritation, and adhesion to skin and may not bestable when exposed to the open atmosphere for long periods of time. Theplasticized assisted sintering of a build material consisting of athermoplastic particulate increases ease of use by offering a method inwhich the process can be automated or semi-automated whereby the articleis immersed in a stable, one component liquid medium for a predeterminedamount of time and allowed to cool to a handling temperature. Stable, asused herein, refers to maintaining a consistent viscosity at apredetermined temperature when exposed to the open atmosphere for a longperiod of time, i.e., on the order of months.

In an aspect, an embodiment of the invention features a powder materialsystem for three dimensional printing including a substantially dryparticulate material including an aqueous-insoluble thermoplasticparticulate material, plaster, and a water-soluble adhesive. The dryparticulate material is suitable for use in three dimensional printingto form an article comprising a plurality of layers, the layersincluding a reaction product of the particulate material and an aqueousfluid that contacts the particulate material during three dimensionalprinting.

One or more of the following features may be included. A static and adynamic friction coefficient of the particulate material possess arelationship defined by a Bredt parameter having a value in excess of0.1. An internal angle of friction may be selected from a range of 40°and 70°. The particulate material may include about 5%-50% by weight ofthe aqueous-insoluble thermoplastic, about 25-90% by weight of theplaster, and about 5-30% by weight of a water-soluble adhesive. Theaqueous-insoluble thermoplastic may include or consist essentially ofhigh molecular weight polyethylene, polyamide, poly-cyclic-olefins,and/or combinations thereof.

The particulate material may further include a processing aid, e.g., theparticulate material may include about 0.01-2.0% by weight of theprocessing aid. The processing aid may include or consist essentially ofmineral oil, propylene glycol di(caprylate/caprate), petroleum jelly,propylene glycol, di-isobutyl phthalate, di-isononyl phthalate,polyalkyleneoxide modified heptamethyltrisiloxanes, polyalkyleneoxidemodified polydimethylsiloxanes, and/or combinations thereof.

In another aspect, an embodiment of the invention features a kitincluding a substantially dry particulate material including anaqueous-insoluble thermoplastic particulate material, plaster, and awater-soluble adhesive. The kit also includes an aqueous fluid binderand an infiltrant.

One or more of the following features may be included. The infiltrantmay include 0-99.99% by weight hydroxylated hydrocarbon, 0-99.99% byweight a solid wax, 0-99.99% by weigh a plasticizer, and 0.01-5% byweight a stabilizer.

The hydroxylated hydrocarbon may include a hydrocarbon diol with amolecular weight greater than 118 g/mol, a melting point greater than30° C., and a kinematic viscosity of 150 centiStokes or less, preferably50 centiStokes or less, at a temperature of at least 50° C. Thehydrocarbon diol may include or consist essentially of octane dioland/or decane diol.

The infiltrant may include hydroxylated hydrocarbon that includes (i) ahydrocarbon diol with a molecular weight greater than 118 g/mol and amelting point greater than 30° C. and (ii) a plasticizer. Thehydroxylated hydrocarbon may include decane diol. The plasticizer mayinclude or consist essentially of benzene sulfonamide and/or propylenecarbonate.

The hydroxylated hydrocarbon may include an alcohol with boiling pointselected from a range of 25° C. to 100° C., and the plasticizer may havea boiling point selected from a range of 25° C. to 100° C. The alcoholmay include or consist essentially of isopropanol. The plasticizer mayinclude or consist essentially of ethanol.

In yet another aspect, an embodiment of the invention includes a methodfor forming an article by three dimensional printing. The methodincludes (i) providing a particulate material comprising a plurality ofadjacent particles, the particulate material comprising anaqueous-insoluble thermoplastic; (ii) applying to at least some of theplurality of particles an aqueous fluid binder in an amount sufficientto bond those particles together to define the article; and (iii)immersing the article in a liquid infiltrant medium.

One or more of the following features may be included. The liquidinfiltrant medium may include a hydroxylated hydrocarbon. The liquidinfiltrant medium may also include a plasticizer. The particulatematerial may further include at least one of plaster, a water-solubleadhesive, a retarder, an accelerator, and a processing aid.

In another aspect, an embodiment of the invention features anessentially solid article manufactured by a three-dimensional printingprocess, the essentially solid article comprising a product of areaction between (i) a substantially dry particulate material includingan aqueous-insoluble thermoplastic particulate material, plaster, and awater-soluble adhesive; (ii) an aqueous fluid comprising water, ahumectant, a rheology modifier, a surfactant, a preservative, and anoptical brightening agent; and (iii) an infiltrant including ahydroxylated hydrocarbon, a wax, a plasticizer, and a stabilizer. Theaqueous-insoluble thermoplastic particulate material material isplasticized by the infiltrant.

In still another embodiment, an article includes a product of (i) asubstantially dry particulate material including an aqueous-insolublethermoplastic particulate material, plaster, and a water-solubleadhesive; and (ii) an infiltrant.

The article preferably has a strength of at least 5 megapascal (MPa),more preferably at least 15 MPa, and most preferably at least 20 MPa.

BRIEF DESCRIPTION OF THE FIGURES

The following drawings are not necessarily to scale, emphasis insteadbeing placed generally upon illustrating the principles of theinvention. The foregoing and other features and advantages of thepresent invention, as well as the invention itself, will be more fullyunderstood from the following description of exemplary and preferredembodiments, when read together with the accompanying drawings, inwhich:

FIG. 1 is a schematic view of a first layer of a mixture of particulatematerial of an embodiment of the invention deposited onto a downwardlymovable surface of a container on which an article is to be built,before any fluid has been delivered;

FIG. 2 is a schematic view of an ink-jet nozzle delivering a fluid to aportion of the layer of particulate material of FIG. 1 in apredetermined pattern;

FIG. 3 is a schematic view of a final article of an embodiment of theinvention enclosed in the container, the article made by a series ofsteps illustrated in FIG. 2 and still immersed in the loose unactivatedparticles;

FIG. 4 is a schematic view of the final article of FIG. 3;

FIG. 5 is a graph illustrating an estimated solubility range of TROGAMIDT-5000;

FIG. 6 is a schematic illustration of a circulating spreader bead;

FIGS. 7 a, 7 b, and 8 are graphs illustrating the forces acting on aparticle during three dimensional printing;

FIG. 9 a is a CAD drawing of the article portion printed in FIGS. 9 band 9 c;

FIGS. 9 b and 9 c are laser profilometer images comparing the effect ofparticulate materials with high internal angle of friction on finishedarticle properties;

FIG. 10 a is a CAD drawing of the article portion printed in FIGS. 10 band 10 c; and

FIGS. 10 b and 10 c are laser profilometer images comparing the effectof particulate material with low internal angle of friction on finishedarticle properties.

DETAILED DESCRIPTION Three Dimensional Printing

Referring to FIG. 1, in accordance with a printing method using thematerials system of the present invention, a layer or film of aparticulate material 20, i.e., a powder, is applied on a linearlymovable surface 22 of a container 24. The layer or film of particulatematerial 20 may be formed in any suitable manner, for example using acounter-roller. The particulate material 20 applied to the surfaceincludes an aqueous-insoluble thermoplastic particulate material,plaster, and a water-soluble adhesive. The particulate material 20 mayalso include a filler material, a processing aid material, and/or afibrous material.

Referring to FIG. 2, an ink-jet style nozzle 28 delivers an activatingfluid 26, i.e., an aqueous fluid described below, to at least a portion30 of the layer or film of the particulate mixture 20 in atwo-dimensional pattern. According to the printing method, the fluid 26is delivered to the layer or film of particulate material 20 in anypredetermined two-dimensional pattern (circular, in the figures, forpurposes of illustration only), using any convenient mechanism, such asa drop-on-demand (DOD) printhead driven by software in accordance witharticle model data from a computer-assisted-design (CAD) system.

The first portion 30 of the particulate mixture is activated by thefluid 26, causing the activated particles to adhere together to form aconglomerate of the particulate material 20 (powder) and fluid 26. Theconglomerate defines an essentially solid circular layer that becomes across-sectional portion of an intermediate article 38 (see, e.g., FIGS.3 and 4). As used herein, “activates” is meant to define a change instate from essentially inert to adhesive.

This definition encompasses the activation of the adhesive particulatematerial to bond the absorbent filler particulate material. When thefluid initially comes into contact with the particulate mixture, itimmediately flows outwardly (on a microscopic scale) from the point ofimpact by capillary suction, dissolving the adhesive within a relativelyshort time period, such as the first few seconds. A typical droplet ofactivating fluid has a volume of about 40 picoliters (pl), and spreadsto a diameter of about 100 μm after coming into contact with theparticulate mixture. As the solvent dissolves the adhesive, the fluidviscosity increases dramatically, arresting further migration of thefluid from the initial point of impact. Within a few minutes, the fluidwith adhesive dissolved therein infiltrates the less soluble andslightly porous particles, forming adhesive bonds between the absorbentfiller particulate material as well as between the additional filler andthe fiber. The activating fluid is capable of bonding together an amountof the particulate mixture that is several times the mass of a dropletof the fluid. As volatile components of the fluid evaporate, theadhesive bonds harden, joining the absorbent filler particulate materialand, optionally, additional filler and fiber particulates into a rigidstructure, which becomes a cross-sectional portion of the final article40. Thus, the layers include a reaction product of the particulatematerial and the activiating fluid, e.g., an aqueous fluid.

Any unactivated particulate mixture 32 that was not exposed to the fluidremains loose and free-flowing on the movable surface 22. Theunactivated particulate mixture is typically left in place untilformation of the intermediate article 38 is complete. Leaving theunactivated, loose particulate mixture in place ensures that theintermediate article 38 is fully supported during processing, allowingfeatures such as overhangs, undercuts, and cavities to be defined andformed without the need to use supplemental support structures. Afterformation of the first cross-sectional portion of the intermediatearticle 38, the movable surface 22 is indexed downwardly, in thisembodiment, and the process is repeated.

Using, for example, a counter-rolling mechanism, a second film or layerof the particulate mixture is then applied over the first layer,covering both the rigid first cross-sectional portion, and any proximateloose particulate mixture. A second application of fluid follows in themanner described above, dissolving the adhesive and forming adhesivebonds between at least a portion of the previous cross-sectional formedportion, the absorbent filler particulate material, and, optionally,additional filler and fiber of the second layer, and hardening to form asecond rigid cross-sectional portion added to the first rigidcross-sectional portion of the final article. The movable surface 22 isagain indexed downward.

The previous steps of applying a layer of particulate mixture, includingthe adhesive, applying the activating fluid, and indexing the movablesurface 22 downward are repeated until the intermediate article 38 iscompleted. Referring to FIG. 3, the intermediate article 38 may be anyshape, such as cylindrical. At the end of the process, only a topsurface 34 of the intermediate article 38 is visible in the container24. The intermediate article 38 is typically completely immersed in asurrounding bed 36 of unactivated particulate material. Alternatively,an article could be formed in layers upward from an immovable platform,by successively depositing, smoothing, and printing a series of suchlayers.

Referring to FIG. 4, the unactivated particulate material may be removedfrom the intermediate article 38 by pressurized air flow or a vacuum.After removal of the unactivated particulate material from theintermediate article 38, a post-processing treatment may be performed,such as cleaning, infiltration with stabilizing materials, painting,etc. to define a final article 40, having the same shape as intermediatearticle 38, but with additional desired characteristics, such as astiffness, strength, and flexibility.

A particularly suitable infiltration method for the particulate materialdescribed herein includes immersing a finished article into a liquidinfiltrant medium, i.e., a plasticizer, to increase the strength andtoughness of the article. After the article is formed, it may besubmerged in a liquid material and then heated to a sinteringtemperature. Alternatively, it may be submerged into a preheatedplasticizer bath, causing in-situ diffusion and sintering.

Preferably the article is completely immersed into the liquid or moltenmaterial. The material may be melted by placing the material in apolypropylene container in an oven, e.g., a Blue M oven or a Cole PalmerStableTemp mechanically convected oven model 52100-00, with the oventemperature being sufficiently high to melt the material. The containeris preferably sufficiently large for the article to be completelysubmerged into a liquid disposed therein. Alternatively, the materialmay be melted by exposure to microwaves. In a preferred embodiment, thearticle is completely submerged until substantially all of the entrappedair rises to the liquid's surface in the form of air bubbles.

Alternatively, liquid or molten material may be sprayed onto the articleusing spray bottles, nozzles, pumps or other means to completely coverthe surface of the article.

The resulting essentially solid article may be the product of thereaction of (i) a substantially dry particulate material including anaqueous-insoluble thermoplastic particulate material, plaster, and awater-soluble adhesive; (ii) an aqueous fluid comprising water, ahumectant, a rheology modifier, a surfactant, a preservative, and anoptical brightening agent; and (iii) an infiltrant comprising ahydroxylated hydrocarbon, a wax, a plasticizer, and a stabilizer, withthe aqueous-insoluble thermoplastic particulate material beingplasticized by the infiltrant. An article may be the product of asubstantially dry particulate material including an aqueous-insolublethermoplastic particulate material, plaster, and a water-solubleadhesive, and an infiltrant. The article may have a strength of at least5 MPa, preferably at least 15 MPa, and most preferably at least 20 MPa.

Particulate Material

In a preferred embodiment, a particulate material, i.e., a substantiallydry particulate material, includes or consists essentially of:

an aqueous-insoluble thermoplastic particulate 5-50 wt % materialplaster (calcium hemihydrate) 25-90 wt % water-soluble adhesive 5-30 wt% retarder 0.01-5 wt % accelerator 0.01-5 wt % processing aids 0.01-2.0wt %

An example of a preferred particulate composition is:

an aqueous-insoluble thermoplastic particulate 15-35 wt % materialplaster (calcium hemihydrate) 50-80 wt % water-soluble adhesive 5-15 wt% retarder 0.01-5 wt % accelerator 0.01-3 wt % processing aids 0.01-2.0wt %

A preferred particle size of components of the particulate material isan average particle diameter of less than 125 microns and greater than10 microns.

The aqueous-insoluble thermoplastic particulate material provides extradurability and increased strength when it sinters together after beingplasticized by the liquid medium. A suitable aqueous-insolublethermoplastic has a particle size greater than 20 microns and less than100 microns, and has a glass transition temperature greater than 45° C.The aqueous-insoluble thermoplastic particulate material also is solubleand/or permeable with certain non-aqueous solvents, waxes, orhydrocarbon diols that can act as plasticizers.

An example of an appropriate aqueous-insoluble thermoplastic particulatematerial is a polyamide 6-3 and terphthalic acid copolymer, availableunder the trade name of TROGAMID, such as TROGAMID T5000 from Degussabased in Germany. According to its technical data sheet, TROGAMID T5000exhibits a resistance to most chemicals; however, it lacks chemicalresistance to certain hydroxylated hydrocarbons like ethanol, propyleneglycol, and pentanediol. TROGAMID T5000 also has decreased chemicalresistance against, e.g., methanol, 1-propanol, pentanol, allyl alcohol,aniline, crotonaldehyde, dimethylformamide, and glacial acetic acid.TROGAMID T5000's weakness to these types of chemicals makes it possibleto use these hydroxylated hydrocarbons as plasticizers with TROGAMIDT5000 to reduce its glass transition temperature to a point where itsinters together in the matrix of the three-dimensional article.

Other suitable aqueous-insoluble thermoplastic particulate materials arehigh molecular weight polyethylene like GUR from Ticona USA based inFlorence, Ky. and cyclic polyolefins like TOPAS from TOPAS AdvancedPolymers. These particular thermoplastics lack chemical resistance toaliphatic and/or aromatic solvents, and/or paraffin based oils andwaxes, rendering these materials suitable for use as plasticizers forthese thermoplastic materials. Yet other examples of aqueous-insolublethermoplastic particulate materials include polyamide andpoly-cyclic-olefins.

The plaster provides dimensional stability and adhesion for strength ofan article formed from the particulate material. A suitable plaster foruse with embodiments of the invention is calcium hemihydrate having aparticle size distribution ranging from greater than 20 microns to lessthan 125 microns. An example of such plaster is HYDROCAL, available fromUSG based in Chicago, Ill. Another suitable plaster product that iswhiter than HYDROCAL is the SSS Brand from San Esu based in Suita,Osaka, Japan. The whiter product imparts a more neutral color toarticles than HYDROCAL, which may be desirable for attaining a widercolor gamut.

The water-soluble adhesive provides adhesive strength in the system andhelps to control bleed or pooling of fluid binder in selectively printedareas. A suitable water-soluble adhesive is a polymer with an averagemolecular weight from a range of 10,000 to 200,000 g/mol with hydrolysisgreater than 85% and less than 90% and a particle size distributionranging from greater than 5 micron to less than 125 microns. Awater-soluble adhesive is a polyvinyl alcohol such as CELVOL 203Savailable from Celanese from Dallas, Tex. Another suitable resin is amaltodextrin such as STAR-DRI-1, available from A. E. Staley based inDecatur, Ill. Maltodextrin may be used to improve the stiffness of thearticle as it is drying and during the post processing with a liquidmedium infiltrant.

A retarder may be included, such as borax. After an aqueous binder isdeposited onto a plaster-containing particulate material, calciumsulfate dihydrate crystals form during gypsum setting. Retarders helpdecrease the growth rate of calcium sulfate dihydrate crystals, thusreducing a distortion effect known as arching in three dimensionalprinting. Arching is a distortion defect in which flat bottom surfacesexhibit concavity from successive layers expanding too fast.

An accelerator may be included, such as potassium sulfate, potassiumaluminum sulfate, sodium sulfate, calcium sulfate dihydrate, or aluminumsulfate. The accelerator helps increase the precipitation rate ofaqueous calcium sulfate into calcium sulfate dihydrate to gain anappreciable early handling strength.

Processing aids may be used to affect particulate material spreadingcharacteristics to achieve a desirable Bredt parameter (see discussionbelow) and to reduce dust becoming airborne while the powder is beingused. Mineral oil is a typical processing aid that affects the Bredtparameter of the particulate material. Mineral oil from Sigma-Aldrichmay provide a good balance of particulate cohesion and low plasticizingof the aqueous-insoluble filler. Other examples of processing aidsinclude propylene glycol di(caprylate/caprate), petroleum jelly,propylene glycol, di-isobutyl phthalate, di-isononyl phthalate,polyalkyleneoxide modified heptamethyltrisiloxanes, polyalkyleneoxidemodified polydimethylsiloxanes, and combinations thereof.

Fluid Binder

In a preferred embodiment, a fluid binder is an aqueous fluid thatincludes or consists essentially of:

water 70-90 wt % humectant 1-10 wt % preservative 0.05-5 wt % surfactant0-2 wt % optical brightening agent 0-5 wt %The aqueous fluid may also include rheology modifiers at a concentrationof 0.01-5 wt %. As discussed below, the aqueous fluid may include afluorescent brightener based on stilbene chemistry or distyrylbiphenyl.

Humectants may serve to keep the nozzles of the print head from dryingout and forming a crust when uncapped, such as during the period whenthe print head is not firing droplets but moving over the build area toa new position. The type and concentration of a humectant may alsoinfluence the dynamics of droplet formation, the consistency of droptrajectory, and the curing of the article formed by three dimensionalprinting. Examples of suitable humectants include Glycerol and otherdiols from 3-10 carbons long; many other examples of humectants areknown in the art. Printing may be successful with humectant levels from1-20%, depending on the binder formulation.

The preservative may serve to prolong the shelf life of the fluid asmanufactured, as well as to extend its useful life in the machine.Preservatives may have detrimental effects on print quality, and in somecases on the appearance or curing of the article being formed by threedimensional printing. It is generally desirable to chooseenvironmentally friendly, stable, and substantially clear preservatives.An example of a suitable preservative includes Proxel GXL, manufacturedby Arch Chemical. Many other suitable preservatives are available in theindustry.

Surfactants are typically used to control the surface tension of theaqueous fluid. Proper surface tension helps ensure that the dropletsbeing ejected from a print head are formed with a consistent volume,depart from the print head at the appropriate vector, and do not formsatellite drops. Very high surface tension may create poor wetting whenthe binder impacts loose powder. Low surface tension may create poordroplet formation at the face of the print head. Surface tensions ofsuitable binders for use with an HP11 print head (from Hewlett-Packard)range from 30 dynes/cm to 36 dynes/cm. Suitable surfactants includeSurfynol CT-171, Surfynol 465, and Surfynol 485 in ranges from 0.24 wt %to 1.5 wt %. Such products are available from Air Products. The range ofviscosities of the aqueous fluid suitable for use with HP11 print headsis 1-1.35 cps. pH of the fluid may also influence the safety of theproduct, the effect of the binder on the reaction rate of the plaster,and the compatibility of the fluid with the materials from which themachine is constructed. An acceptable range of pH for the aqueous fluiddescribed herein is, e.g., from 4.9 to 10.3.

The aqueous fluid may be used for three dimensional printing, such thatan article printed with the aqueous fluid including the opticalbrightening agent has a lower chroma C* than an article printed with theaqueous fluid without the optical brightening agent. Optical brightenersare used to color correct the whiteness of a three-dimensional printedpart. Optical brightening agents increase the perceived whiteness of apart by absorbing ultra violet light having a wavelength <400 nanometers(nm) and re-emitting blue light with a wavelength typically selectedfrom a range of 400 to 450 nm, increasing the reflected light in thevisible spectrum. The blue fluorescence of the optical brightener helpsto overcomes the natural yellowness of the other raw materials.Quantitatively, this may be expressed as higher emission in the bluereflectance.

Liquid Infiltrant Medium

In one preferred embodiment, a liquid infiltrant includes or consistsessentially of:

a hydroxylated hydrocarbon 0-99.99 wt % a wax (solid at roomtemperature) 0-99.99 wt % a plasticizer 0-99.99 wt % stabilizer  0.01-5wt %

For example, the liquid infiltrant may include or consist essentiallyof:

a hydroxylated hydrocarbon (solid at room 69.99-99.99 wt % temperature)a plasticizer 0-30 wt % stabilizer 0.01-5 wt %

In another embodiment, a liquid infiltrant may include or consistsessentially of:

a paraffin wax (solid at room temperature) 79.99-99.99 wt % aplasticizer 0-20 wt % stabilizer 0.01-5 wt %

In another preferred embodiment, a liquid infiltrant includes orconsists essentially of:

a fugitive hydroxylated hydrocarbon (liquid at 30-100 wt %  roomtemperature) a solvent 0-50 wt % a plasticizer 0-30 wt %

The hydroxylated hydrocarbon may be the primary plasticizer that reducesthe glass transition temperature of the aqueous-insoluble thermoplasticparticulate material. The hydroxylated hydrocarbon may also be thecarrier of a secondary plasticizer that is soluble in the hydroxylatedhydrocarbon and more effective in plasticizing the aqueous-insolublethermoplastic, and where the hydroxylated hydrocarbon is less effectivein plasticizing the aqueous-insoluble thermoplastic. Suitablehydroxylated hydrocarbons are ethanol, pentane-diol, octane-diol, anddecanediol.

Ethanol, having a boiling point below 100° C., is a suitable fugitiveplasticizer for the TROGAMID T5000; ethanol evaporates away from theprinted article after infiltrating the article, with the TROGAMID T5000sintering together within the matrix of the article. Ethanol may be tooeffective in plasticizing TROGAMID T5000 to an extent that an articlemay distort and collapse under its own weight. The plasticizing effectof ethanol may be reduced by adding another miscible hydroxylatedhydrocarbon having a boiling point less than 100° C. such asisopropanol. Isopropanol does not exhibit the same plasticizing effecton TROGAMID T5000, and is fugitive as well having a boiling point wellbelow 100° C. The addition of isopropanol to ethanol may decrease thehydrogen bonding forces of the ethanol, thereby possibly decreasing theplasticization effect of the alcohol mixture on TROGAMID T5000. However,the use of hydroxylated hydrocarbons with boiling points less than 100°C. may raise concerns of flammability and end-user safety. Octane dioland decane diols are generally more preferred hydroxylated hydrocarbonsbecause they have higher flashpoints than ethanol, and are solid at roomtemperature and are liquid with a kinematic viscosity of 150 centiStokesor less, more preferably 50 centiStokes or less at temperatures greaterthan 50° C.

A solid wax having a melting point greater than 30° C. may be theprimary plasticizer to reduce the glass transition temperature (T_(g))of the aqueous-insoluble thermoplastic, or may be the carrier of asecondary plastics that is soluble in the solid wax when in a melted,liquid state at temperatures above 50° C. if the solid wax is noteffective in lowering the T_(g) of the aqueous-insoluble thermoplasticalone. Suitable waxes that plasticize TROGAMID T5000 are hydrocarbondiols with molecular weights greater than 118 g/mol, such as octane dioland decane diol. Another suitable solid wax is paraffin wax such asParaplast X-Tra available from McCormick Scientific based in St. Louis,Mo., which is suitable for plasticizing both polyethylene thermoplasticslike GUR and cyclic-poly-olefins like TOPAS. At a temperature of atleast 50° C., the wax may have a kinematic viscosity of 150 centiStokesor less, preferably 50 centiStokes or less, to ensure a fastinfiltration rate and deep penetration into an immersed article; and tofacilitate easier drainage and removal of excess liquid infiltrant fromthe article when the article is extracted from the liquid infiltrant,thereby reducing pooling and drip defects on the article as the waxsolidifies.

The plasticizer may be the sole ingredient or an additive in either ahydroxylated hydrocarbon and/or a solid wax to enhance theplasticization of the aqueous-insoluble thermoplastic particulatematerial. The plasticizer may be the sole ingredient that is in a liquidstate when infiltrating a three dimensional article. Suitable soleplasticizers are, for example, ethanol, octane diol, and decane diol forreducing the T_(g) of TROGAMID T5000. Paraffin waxes and mineral oil mayalso be suitable as sole plasticizers for polyethene and poly-cyclicpoly olefins such as GUR and TOPAS respectively. A suitable mineral oilfor use with an embodiment of this invention is supplied by Aldrichbased in Milwaukee, Wis. The plasticizer may be used as an additive whensupplied in a soluble carrier at a concentration less than 20% byweight. A suitable plasticizer used as an additive may be ethanolcarried in isopropanol, or, more preferably, benzene sulfonamide carriedin decane diol to assist the plasticization of TROGAMID T5000. Othersuitable plasticizer additives may be used, such as ones based oncarbonates, succinates, phthalates, adipates, and phosphates.

Stabilizers may be added to the liquid infiltrant medium to decreaseoxidation that may lead to the discoloration of the liquid infiltrantmedium when kept at temperatures above 50° C. for prolonged periods oftime. Suitable stabilizers are antioxidants such as butylatedhydroxytoluene.

Mechanisms of Plasticizer-Assisted Sintering

A summary of a printing/infiltration process is as follows:

a) a layer is formed of a substantially dry particulate materialcontaining thermoplastic particulate, a plaster, and/or a water-solublepolymer such as a water-soluble adhesive;

b) an aqueous fluid binder is applied to the layer of dry particulatematerial in a predetermined pattern to cause binding in the areas towhich the binder is applied;

c) steps (a) and (b) are repeated sequentially to define athree-dimensional article;

d) after complete setting of the thermoplastic, plaster, orwater-soluble polymer, the three-dimensional article is removed from thebuild, i.e., from the stack of dry particulate material layers;

e) the three-dimensional article is submerged in the plasticizer or itssolution, i.e., the liquid infiltrant medium, at ambient or elevatedtemperature; and

f) optionally, the particulate material is exposed to additional energyin the form of conventional heat, visible or infrared light, microwave,or radio-frequency, for additional sintering of particulate material.

The use of certain infiltrant materials (such as plasticizers) describedherein allows selective diffusion into the polymer matrix duringinfiltration to reduce the glass transition temperature and to increasethe melt flow of the aqueous-insoluble polymer. This also results in thereduction of the inert, non-water-soluble polymer concentration in orderto achieve good green strength and sagging resistance.

In an embodiment, articles are submerged into a liquid infiltrant mediumand heated to the sintering temperature. In another embodiment, articlesmay be submerged in a preheated plasticizer bath causing in-situdiffusion and sintering. The sintering may be performed withoutapplication of additional pressure, i.e., the sintering may besubstantially pressure-free.

In yet another embodiment, rather than being provided as a liquidinfiltrant, the plasticizer may be a component of the particulatecomposition. Alternatively , the article may be placed in a heatedchamber filled with plasticizer in the gaseous phase.

The particulate composition may include an inert absorbent filler issaturated with plasticizer. Here, after an article is printed, theplasticizer migrates into the polymer matrix during heat treatment.

The plasticizer may be applied as a pure substance, solution oremulsion. It may also contain solvents, surfactants, viscositymodifiers, dyes, and/or pigments.

The plasticizer may be liquid or solid at room temperature. Solidplasticizer may be applied to the particulate composition in the moltenform. Use of plasticizers with high melting point typically diminishesor prevents their migration during the lifetime of an article. Liquidplasticizer may be dissolved in a high melt temperature inert solidcarrier, creating material that is solid at room temperature.

One of the advantages of the processes described herein is that one mayproduce both rigid and rubbery articles from the same particulatecomposition by employing a different plasticizer system or a system thatcontains different concentrations of the same plasticizers. Also,uniformly colored articles may be produced by dissolving dyes in theliquid or solid plasticizer systems.

Solubility of the plasticizer in the polymer matrix of the article isdetermined by the polymer system, and depends on three major parameters.These parameters are: interaction between plasticizer molecules; themolecular interaction between the polymer molecules; and the mutualinteraction of the polymer molecules when mixed. Most commonly, thoseinteractions may be calculated using the Hansen solubility parameters.These parameters allow for accurate estimation of solubility andswelling of the polymers in solvents, or in this case plasticizers. Inparticular, the Hansen solubility parameters represent the followingintermolecular forces, the so-called Van der Waals forces: dispersionforces (δ_(d)), dipole—dipole interactions (δ_(p)) and hydrogen bondingforces (δ_(h)). The total Hildebrand solubility parameter (δ) may becalculated with these components as follows:

δ=(ι_(d) ²+δ_(p) ²+δ_(h) ²)^(1/2)

The concepts presented here regarding the Hildebrand and Hansensolubility parameters may be found in the Polymer Handbook, Brandup, J.et. al., John Wiley & Sons, Inc., 1999, the disclosure of which isincorporated herein by reference in its entirety. A close quantitativeagreement between the Hansen solubility parameters of the polymer andthe Hansen solubility parameters of the plasticizer implies greatersolubility of the plasticizer into the polymer, thus lowering the energytypically required for sintering.

Extremely high solubility of the polymer in plasticizer may beundesirable because this may result in over-plasticization or thedissolution of the thermoplastic additive. In that case, the glasstransition temperature may be close or below room temperature, which maycause distortion and weak particle bonding. In some embodiments,plasticizer material may be preferably selected from materials that havelow solubility at room temperature but greater solubility at highertemperatures.

To reduce solubility, the plasticizer may be diluted either by thesolvent that is removed after sintering or inert solid material that mayremain in the three dimensional article after cooling.

As an example of how one may select a plasticizing solvent, chemicalresistance data was acquired from Degussa's TROGAMID T5000 productliterature and the Hansen solubility parameters of the solvents wereestimated using the Hoy group contribution method as described in thePolymer Handbook, to produce the data given in Table 1:

TABLE 1 Solvent Effect δd δp δh allyl alcohol dissolves 13.5 12.5 22amyl alcohol dissolves 14.6 9.3 16.9 Aniline dissolves 16.3 13.1 10.6n-butyl alcohol dissolves 14.4 10.1 18.5 Crotonaldehyde dissolves 14.111.2 15.2 dimethyl formamide dissolves 12.6 10.4 12.2 ethylene diaminedissolves 13.6 14.5 18 formic acid dissolves 13.3 13.1 26.3 furfuralalcohol dissolves 14 13.7 22.1 acetic acid dissolves 13.9 10.4 16.6isoamyl alcohol dissolves 14.3 9.3 16.3 n-propanol dissolves 14.2 1120.9 adipinnic acid no effect 14.8 10.5 11.9 amyl acetate no effect 15.37.7 10.5 Anisole no effect 17.1 10.7 12.4 Benzene no effect 17.5 9.2 8.1butyl acetate no effect 15.2 8.2 11 t-butyl methyl ether no effect 15.25.6 9.2 carbon tetrachloride no effect 14.4 17.9 9.4 dibutylphthalate noeffect 15.3 9.5 9.5 1,2 dichlorobenzene no effect 18.2 9.9 6.2difluorodichloromethane no effect 31.1 18.7 25.3 si-isobutyl ketone noeffect 15.1 7.1 9 di isopropyle ether no effect 15.4 5.2 9 ethyl acetateno effect 14.7 9.5 12.9 ethyl benzene no effect 17.5 7.8 6.3 ethyl etherno effect 15.6 6 12 formaldehyde no effect 12.5 15.5 31.9 isooctane noeffect 15.9 0 5.8 n-heptane no effect 15.2 0 4.9 n-hexane no effect 15.20 5.6 hexane triol no effect 12.1 12.4 23.3 Toluene no effect 17.4 8.57.2 trichloroethylene no effect 15.4 16.4 10.4 acrylonitrile stresscrack 12.5 14.2 19.5 benzaldehyde stress crack 15.8 12.9 11.3 1,3 butanediol stress crack 12.6 12.5 23.5 1,4 butane diol stress crack 13.1 13.124.9 2,3 butane diol stress crack 12.1 11.8 22 t-butyl alcohol stresscrack 13.8 10.1 16.7 Chloroform stress crack 14.7 15.9 12.8 1,2dichloroethylene stress crack 15 13.7 14 Ethanol stress crack 13.8 12.324.5 Isopropanol stress crack 13.8 11 20 methyl ethyl ketone stresscrack 14.6 9.8 13.6 propylene glycol stress crack 12.4 14.3 27.3

From this table, one can plot a solubility range for TROGAMID T5000 byplotting the hydrogen bonding forces, δ_(h), against the combined valueof the dispersion and polar forces, (δ_(d) ²+δ_(p) ²)^(1/2) solventwithin a radius of 5)as shown in FIG. 5. In accordance with a heuristic,any (MPa)^(1/2) of a polymer's solubility parameter location on theδ_(h) vs (δ_(d) ²+δ_(p) ²)^(1/2) plot is to be considered a solvent thatwill interact with the polymer, and any solvent outside that radiustypically does not have any effect. The solubility parameters forTROGAMID T5000 in this example may also be estimated from the Hoycontribution method. One can see in FIG. 5 that solvents that have noeffect (represented by X), as indicated in the TROGAMID T5000 productliterature, lie at or beyond the radius of interaction (indicated by alarge oval), while solvents that affect the polymer (represented by ∘and ε, as well as octanediol and decanediol) fall within the radius withsome extending upwards outside the radius as the hydrogen bonding forcesincrease. This suggests that solvents with high hydrogen bonding forcesare more significant in polymer-solvent interaction for this particularexample. When the hydroxylated hydrocarbons of interest in certainembodiment, i.e., decanediol and octanediol, are plotted using the Hoycontribution method, one can see that they fall within the radius ofinteraction of TROGAMID T5000, and may, therefore, impart the desiredplasticizing effect.

EXAMPLES Example 1

One kilogram of particulate material was prepared using the materialsand ratios shown below in Table 2. The mixture was placed in a KitchenAid Professional 600 Mixer and mixed for about 20 minutes. The resultingblended mixture was then sieved through a 50 mesh screen to removeclumps.

TABLE 2 Percent Ingredient (weight) Material/Trade Name Vendor/GradePlaster 52.3 HYDROCAL U.S. Gypsum Plastic 42.9 TROGAMID T5000 DegussaAdhesive 4.2 Polyvinyl Alcohol Cleanese Accelerator 0.2 PotassiumSulfate Aldrich Accelerator 0.4 Terra Alba U.S. Gypsum

Flexural strength test bars 50 mm long, 5 mm wide, and 5.7 mm tall wereprinted on Z310 using zb58 binder with a-binder-to-volume ratio of 0.10.The test bars were dried for 2 hours at 38° C. in an oven. Sequentially,test bars were infiltrated by dipping them in different alcohols(solvents) for 15 seconds at room temperature, removing them from thesolvents, and placing them in an oven (Cole Palmer StableTempmechanically convected oven model 52100-00) preheated to 75° C. for 3hours. After the test bars were cooled at ambient conditions for 1 hour,they were placed and supported on a 2-point span spaced at 40 mm. Aforce was applied on the top of the bar at the center of the 40 mm spanusing a Texture Analyzer TA-XT2 from Texture technologies (Scottsdale,N.Y.). The maximum force applied at which the bars break was recordedand used to calculate the measured bar strengths given in Table 3. Asone can see from the table, the use of an infiltrant greatly increasedthe resulting bar strength.

TABLE 3 Infiltrant Z Corporation bar strength (MPa) None 1.0 Ethanol17.0 n-propanol 17.7 Methanol 19.9

Example 2

Powdered material was prepared according to the procedure described inExample 1, using the materials and ratios shown below in Table 4.

TABLE 4 Percent Ingredient (weight) Material/Trade Name Vendor/GradePlaster 47.2 HYDROCAL U.S. Gypsum Plastic 47.2 TROGAMID T5000 DegussaAdhesive 4.1 Polyvinyl Alcohol Cleanese Accelerator 1.0 PotassiumSulfate Aldrich Accelerator 0.5 Terra Alba U.S. Gypsum

Flexural strength test bars describe in Example 1 were printed on Z310particulate material using zb58 binder with a binder to volume ratio of0.25. Parts were dried for 2 hours at 38° C. in an oven. Sequentially,parts were infiltrated by dipping them in different liquids for 15seconds at room temperature. Then parts were removed from the solventand placed in a microwave oven (Sharp Carousel model R2A57 700W). Partswere microwaved for 5 minutes at “High” settings. After parts cooled atambient conditions for 1 hour, the flexural strengths were acquired asdescribed in Example 1, and are reported in Table 5.

TABLE 5 Infiltrant Z Corporation bar strength (MPa) None 0.9 40% Ethanolin acetone 20.4 15% Dipropylene glycol in 15.6 isopropanol

The same dry uninfiltrated flexural strength test bars were placed in apreheated bath contained 1,10-decanediol preheated to 85° C. for 10seconds, removed and left for 16 hours in the oven at 85° C. Theflexural strength test indicated a strength of 28.1 MPa.

Example 3

Powdered material was prepared according to the procedure described inthe Example 1 using the materials and ratios shown below in Table 6.

TABLE 6 Percent Ingredient (weight) Material/Trade Name Vendor/GradePlaster 51.8 HYDROCAL U.S. Gypsum Plastic 38.3 TROGAMID T5000 DegussaAdhesive 6.6 Polyvinyl Alcohol Cleanese Accelerator 2.5 PotassiumSulfate Aldrich Accelerator 0.8 Terra Alba U.S. Gypsum

Flexural strength test bars described in Example 1 were printed on Z310particulate material using zb58 binder with a binder to volume ratio of0.23. Parts were dried for 2 hours at 38° C. in an oven. Parts werecompletely dipped in the heated bath containing molten materials for 10seconds, removed from the molten material and placed in the oven. Theflexural strength results are indicated in Table 7.

TABLE 7 Z Corporation Temperature Exposure time bar strengthInfiltration material ° C. (hr) (MPa) None 80 1 3.3 1,10- decanediol 801 19.8 17% n-butyl benzene 70 1 20.9 sulfonamide in 1,10-decanediol 1,8-octanediol 80 2 22.6

Example 4

A powdered material may be prepared according to the procedure describedin the Example 1 using the materials and ratios shown below in Table 8.

TABLE 8 Percent Ingredient (weight) Material/Trade Name Vendor/GradePlaster 58.0 HYDROCAL U.S. Gypsum Plastic 20.0 TROGAMID T5000 DegussaPlasticizer 10.0 Hydrocarbon diol, e.g., Sigma-Aldrich 1,10-DecanediolAdhesive 8.0 Polyvinyl Alcohol Cleanese Accelerator 3.0 PotassiumSulfate Aldrich Accelerator 1.0 Terra Alba U.S. Gypsum

Articles may be created from the particulate material formulation listedin Table 8 using zb58 aqueous fluid binder with a Z310 printer. Thearticle may then be removed from the Z310 printer 2 hours after printinghas been completed and the article placed in a mechanical convectionoven set between 75° C. to 100° C. for 0.5 to 2 hours to melt thehydrocarbon diol within the article, to plasticize the plastic andfacilitate sintering.

Kits

A preferred kit includes a powder adapted for three dimensionalprinting, an aqueous fluid for activating water soluble components ofthe three-dimensional printing powder, and an infiltrant suitable forplasticizing an aqueous-insoluble thermoplastic component of theparticulate material. The powder may include a loose, dry, andsubstantially free-flowing particulate mixture including anaqueous-insoluble thermoplastic particulate material, plaster (calciumhemihydrate), water-soluble adhesive, and, optionally, a retarder,accelerator, and/or processing aids. The aqueous fluid binder mayinclude water, a humectant, a preservative, and, optionally, asurfactant, and/or an optical brightening agent. The infiltrant mayinclude a hydroxylated hydrocarbon, a solid wax, a plasticizer, and astabilizer.

The particulate material is adapted for use in three dimensionalprinting to form an article comprising a plurality of layers, the layersincluding a reaction product of the particulate material and the aqueousfluid that contacts the particulate material during three dimensionalprinting. The aqueous fluid may be substantially clear, have a viscosityselected from a range of 1-1.35 cps, a surface tension selected from arange of 30-36 dynes/cm, and a pH selected from a range 4.9 to 10.3. Theinfiltrant may be adapted to plasticize the aqueous-insolublethermoplastic particulate material by lowering the glass transitiontemperature of the aqueous-insoluble thermoplastic particulate to allowthe sintering of those particulates. The kit may also include acombination of aqueous fluids comprising cyan, magenta, and yellowcolorants.

The aqueous binder may be selected such that it is capable of hydratingthe plaster (calcium hemihydrate) and initiating the precipitation intoa gypsum cement. The binder is applied onto the substantially dryparticulate material so as to occupy from 10% to 35% of the volumedefined by the selectively printed area at a predetermined layerthickness, typically 100 microns. The printed area is then allowed toset to attain a flexural strength of at least 1 MPa, for example after 2hours from the time the last layer was printed.

An infiltrant that is selected to plasticize the aqueous-insolublethermoplastic particulate material is preferably clear and translucentto allow the natural lightness and color of the powder to show through.The infiltrant may also be selected so as to not interact with theselectively printed areas where aqueous fluid colorants were applied sothat the colors do not migrate out of or through the article. Theinfiltrant may be selected to have a kinematic viscosity of 150centiStokes or less when in a liquid state at a predeterminedtemperature.

Flow Properties of Build Materials

Compositions have been disclosed above that relate to the control of theflow properties of the build material in three-dimensional printers. Thethree principle methods flow property control are the addition of liquid“processing aids,” control of grain size distribution, and the additionof solid fillers that contribute to the frictional behavior of the buildmaterial. Many candidate materials have been disclosed previously, forexample, in U.S. Patent Publication Number 2005/0003189, incorporatedherein by reference in its entirety. Previously, however, the exactimplementation of these methods has been by trial and error. Here, somemechanical properties of dry particulate build materials are disclosedthat are particularly suited for use in three dimensional printing,especially in contrast to other formulations of similar materials forother uses that may not require special flow characteristics of the rawmaterials.

Referring to FIG. 6, in an embodiment of a three-dimensional printer,dry, free-flowing particulate build material is spread by a rotatingspreader rod 500. The rod rotates in a direction counter to thedirection of motion of the spreading mechanism. A circulating bead 510of build material 32 is pushed in front of a moving rod over astationary bed. For the sake of convenience, the system is shown in theframe of the rod with a moving bed 520 and stationary bead. The bed isassumed to approach the spreader, and the bead of build materialcirculates around a nearly stationary center. One may assume that thebuild material is lifted by the leading surface of the spreader rodbecause it adheres to the rod surface 530. The direction of the flow ofthe build material reverses close to a nip 540, i.e., an interfacebetween the spreading roller 500 and the moving bed 520.

The equilibrium of a small printed feature as it passes directlyunderneath the spreader rod is analyzed. On typical three-dimensionalprinters, the thickness t of a single printed layer of build material 32is approximately 1/100 the radius of the spreader rod. Referring to FIG.7 a, the spreader exerts a compressive stress σ_(zz) and a shear stressτ_(xz) on the build material directly underneath it. There is also ahorizontal stress component σ_(xx).

One may assume that the horizontal stress applied to the left edge 600of the feature is not opposed by another stress on the right edge 610.The feature is assumed to leave a wake 620 behind it where buildmaterial, after being swept along the upper surface, is unable to wraparound the downstream corner and establish a stress analogous tohydrostatic pressure against the right surface. The horizontal stressapplied to the left may be opposed by a shear stress along the bottomsurface. A free body diagram of the feature is shown in FIG. 7 b,including a hollow cavity 630 formed in the feature wake 620.

It is assumed here that dry, free-flowing particulate build material inmotion possesses a different shear strength than build material that hasbeen allowed to rest for a time. In general, one may expect a differentyield locus for build material in different states of motion. Forpurposes of this derivation, this is expressed here as two differentsets of yield parameters, “static” and “dynamic” values of the cohesionand friction angle.

These properties of particulate materials are amply supported in theliterature. See, for example, B. M. Das, Advanced Soil Mechanics,Hemisphere Pr. 1997, pp. 315-317 or S. Aranson & L. S. Tsimring in ThePhysics of Granular Media, H. Hinrichsen & D. Wolf, eds, Wiley-VCH,(2004) pp. 146-147, incorporated herein by reference in theirentireties.

A force balance on the feature shown in FIG. 8 leads to the equation:

I[C _(s) −C _(d)+σ_(zz)(tan φ_(s)−tan φ_(d))]=L Δτ>tσ _(xx)   (1)

for the feature to remain in place. The normal stress against the bottomsurface of the feature is assumed the same as that against the topsurface. The difference in shear strength between the static values(static yield locus 700) and dynamic values (dynamic yield locus 710)with normal stress σ_(zz) is denoted by Δτ.

“Bredt flow parameter” (Br) is herein defined, expressing, in general,the propensity for printed features to shift in the build area of athree-dimensional printer during spreading of build material:

Δτ/σ_(xx) =Br>t/L≈0.1   (2)

The ratio t/L is slightly arbitrary. One may assume for practicalpurposes that features with a length at least several times the layerthickness (L˜10 times t) are those that are preferably considered inthis model. Layers with thickness of 100 μm are standard inthree-dimensional printing machines that are currently available, andinstability of isolated patches smaller than 1.0 mm may have a minimallydiscernable effect on the appearance of an article.

For the flow conditions most useful for three dimensional printing, thebuild material is non-cohesive, i.e., the cohesion of the particulatematerial is much less than the dynamic pressure of material in flow.Using reasonable values for the bulk density of the build material andspreading speed in a standard ZPrinter®310 three-dimensional printer,one obtains an order of magnitude estimate:

c _(s) ≈c _(d)>>ρ(u+Ωa)²≈600 Pa   (3)

A material having shear strength of this magnitude is a weak gel, suchas yogurt. While it is not “strong” in any sense of the word, it is byno means “free-flowing.” As an additional estimate of the lower bound ofthe cohesion, we may observe that the bead of free-flowing particulatebuild material may be in a state of yielding at the bottom of the pilewhen the counter-roller begins to move it across the build area. In aZPrinter®310 three-dimensional printer, the bead is approximately 1 cmtall. Accordingly, we require the following inequality to hold:

c _(s) ≈c _(d) >>ρgh≈100 Pa   (4)

This is typically a minimum acceptable range for cohesion in aparticulate build material for it to be considered “free-flowing.” Whilethe compressive and shear stress imposed on the build material throughthe motion of the counter-roller may have a magnitude approximately 600Pa, the cohesion is preferably accordingly less than 100 Pa in order forit not to adversely affect the layering of build material.

With the assumption that the cohesion is negligibly small, the followingsimplification may be made:

(tan φ_(s)−tan φ_(d))>t σ _(xx) /L σ _(zz)   (5)

and

$\begin{matrix}{\frac{\sigma_{xx}}{\sigma_{zz}} = \frac{\left( {1 + {\sin \; \varphi_{d}}} \right)}{\left( {1 - {\sin \; \varphi_{d}}} \right)}} & (6)\end{matrix}$

This leads to the equation:

$\begin{matrix}{{\left( {{\tan \; \varphi_{s}} - {\tan \; \varphi_{d}}} \right)\frac{\left( {1 - {\sin \; \varphi_{d}}} \right)}{\left( {1 + {\sin \; \varphi_{d}}} \right)}} = {{Br}_{nc} > 0.1}} & (7)\end{matrix}$

Equation 7 expresses a vitally important feature of free-flowingparticulate build materials that are suitable for use inthree-dimensional printing machines. The quantity on the left, Br_(nc),is termed the “Bredt flow parameter for noncohesive particulatematerials,” and it preferably has a value greater than about 1/10 forsmall printed features to remain stationary during spreading.

Measurement of Static and Dynamic Friction Coefficients

Methods exist for measuring the static yield properties of particulatematerials in shear. See, for example, B. M. Das, Advanced SoilMechanics, Hemisphere Pr. 1997, pp 313-326. It is found, however, thatthe values for the yield parameters φ and c vary with experimentalconditions, and it is preferable to measure the properties in aparticular stress range of interest.

An example of a piece of laboratory equipment that is capable ofmeasuring the static friction characteristics of particulate materialsis the “ShearScan TS12” manufactured by Sci-Tec Inc. This device holds asample of material in a cylindrical cell and applies a vertical load tothe material to consolidate it to a specified level. The device thenapplies a gradually increasing transverse shearing force until itdetects slip in the sample of material. It performs this measurementacross a range of applied loads to develop a yield locus analogous tothose pictured in FIG. 8. Since the instrument measures the shear stressat the instant of rupture, this is the “static” friction in theparticulate material.

An approximate laboratory procedure may provide estimates of the flowparameter for non-cohesive particulate build materials. This may be doneby measuring the angle of repose of a pile of a particulate materialunder static and dynamic conditions. The procedure is executed asfollows. On an unpolished type 304 stainless steel sheet with a 2B millfinish and a dimension of 12 inches square by 0.060 inches in thicknessavailable from McMaster-Carr based in Elmhurst, Ill., a conical pile isformed from a particulate material sample by sprinkling particles veryslowly at a bulk volumetric flow rate of 30±15 mL per minute over onepoint using a 385 mL stainless steel funnel available from Lab SafetySupply in Janesville, Wis. from a height of about 1 cm above the growingtop of the pile. The height of the pile is chosen such that

gh≈(u+ωa)²

This ensures that the stress at the bottom of the heap is inapproximately the appropriate range. For ordinary three-dimensionalprinters manufactured by Z Corporation, this height is roughly 2 inches.

The initial diameter, d, and height, h, of the pile are measured. Theratio 2 h/d is an approximate measure of the static friction coefficienttan φ_(s). Next, a small impact force delivered from an 18-8 stainlesssteel slotted spring pin, ½ inch in diameter and 2.25 inches long with amass of 32.0±0.5 grams available from McMaster-Carr dropped onto theedge of the stainless steel sheet from a height of 0.65±0.02 inches sothe pile collapses. It is typically preferable to deliver to the plate arelatively light impact so that the motion of the pile after the impactis primarily driven by gravity and not by kinetic energy. Two impactsmay be sufficient. The final height and diameter of the collapsed pileare measured, and the ratio 2 h/d is an approximate measure of thedynamic friction coefficient tan φ_(d).

Several particulate samples were measured in this manner, and the dataare presented below in Table 9. The calculated flow parameter is the“noncohesive” form given in equation 7.

TABLE 9 Measurements of flow parameter for various candidate particulatebuild materials Particulate sample tan phi s tan phi d Br_(nc) zp1000.83 0.52 0.11 zp100 0.91 0.45 0.19 zp100 1.00 0.65 0.10 zp130 0.65 0.350.15 zp130 0.74 0.40 0.16 zp130 0.79 0.45 0.14 4F Lucite 0.53 0.28 0.1450 μm Al₂O₃ 0.64 0.44 0.09 Coated glass beads 0.45 0.35 0.05 +10 ppmNeobee M20 0.46 0.32 0.07 +20 ppm Neobee M20 0.52 0.33 0.10 +30 ppmNeobee M20 0.67 0.53 0.05 +40 ppm Neobee M20 0.79 0.69 0.03 +50 ppmNeobee M20 0.78 0.76 0.00 zp100 and zp130 are products marketed by ZCorporation for building appearance models. 4F Lucite from IneosAcrylics has a particle size between 55 μm and 70 μm. Tabular 50 μmAl₂O₃ acquired from KC Industries Glass Beads from Potter's Industries,72 μm grain size, aminosilane surface treatment Neobee M20 was used tocoat glass beads. Neobee M20 from Stepan Industries

As these data approximately show, build materials designed by ZCorporation for three dimensional printing all fall in the same range, alittle bit higher than the required lower bound. Some scatter in theresults is to be expected with this approximate technique. Although thestatic angle of repose of zp100 is higher than in zp130, the flowparameter for the two build materials is nearly the same. In fact,qualitative experience shows that these two products perform about thesame.

Of the other three materials tested, glass spheres alone had the poorestperformance, with a flow parameter of only about 0.05. This, too, issupported by qualitative experience: glass beads alone are unsuitablefor three dimensional printing from the standpoint of spreading.However, glass beads may be mixed with various processing aids and withother particulate materials that may be finer or equal to in particlesize having a non-spherical and irregular particle shape to achieve adesirable Bredt parameter greater than 0.10, thereby being suitable foruse in three dimensional printing.

To illustrate the extreme sensitivity of particulate behavior with evensmall additions of certain chemicals, generally referred to as“processing aids,” a series of data were taken in which tiny (10 ppm)increments of a low-viscosity emulsifier are added to a sample of glassspheres. The flow parameter rises quickly, peaks, and falls away evenmore quickly even though both the static and dynamic friction anglesincrease through the series. The critical point occurs when the dynamicangle of repose transitions from a nearly constant value to a linearlyincreasing value. This shows that there can be rather sharp optima incomposition to obtain useful spreading characteristics.

This test is a fairly useful technique for identifying relativeperformance properties between different candidate materials. Thepreferred method for evaluating flow properties of candidate buildmaterials during formal optimization after the initial selection periodis to test samples of the material on a working three-dimensionalprinter. Certain pathological geometries are known to those experiencedin the art, and they can be evaluated either qualitatively orquantitatively. One particularly useful geometry for observing stabilityduring spreading is a flat plate studded with pegs that are orienteddownward during the build. During printing, the earliest layersaddressed are a series of disconnected patches that are relatively freeto shift in the build material. After these have been formed, a plate isprinted that joins all of the pegs together in a single object. One caneasily examine whether the pegs are uniform and straight, and one canevaluate the quality of spreading on that basis.

Additional Flow Properties of Build Materials

Compositions have been disclosed that relate to control of the flowproperties of the build material in three-dimensional printers. Thethree principal methods are the addition of liquid “processing aids,”control of grain size distribution, and the addition of solid fillersthat contribute to the frictional behavior of the build material. Manycandidate materials have been disclosed previously, for example, in U.S.Patent Publication Number 2005/0003189. Some mechanical properties ofdry particulate build materials are disclosed in the followingdiscussion that are particularly suited for use in three dimensionalprinting, especially in contrast to other formulations of similarmaterials for other uses that do not require special flowcharacteristics of the raw materials.

A method that may be used to quantify a particulate material'ssuitability for three dimensional printing includes placing 1 liter inbulk volume of a particulate material in a metal cylinder with an insidedimension of 6.1 inches, and inside height of 6.2 inches so that theheight of the powder is between 2.5 to 3.0 inches when the cylinder iscapped with a translucent cover and laid on its side (i.e., the heightof the cylinder is horizontal). The drum is then slowly rolled with arotational velocity of 2.5 rotations/min±0.5 rotations/min until thepowder reaches an angle where it avalanches upon itself. The distancethat the drum rolled, s, is recorded and the angle, φ, can be determinedfrom equation 8:

$\begin{matrix}{\varphi = {\frac{s}{r} \cdot \frac{180}{\pi}}} & (8)\end{matrix}$

where r would equal the outside radius of the drum. The angle, θ, is theinternal angle of friction that particulate material has under theseparticular test conditions at a room temperature between 65 to 75° F.Various particulate materials known to have good and bad spreadingcharacteristics are compared using this test method, and desirable rangeof internal angles of friction were determined. Table 10 summarizes theparticulate material compositions that were measured.

TABLE 10 Powder composition Ingredient A B C D E F G H Potter's 84.64%79.72% 100% 99.8% Spheriglass 2530 CP03 Zinc Oxide  4.75% Pigment LuciteElvacite 15.00% 15.19% 2014 Mineral Oil  0.19%  0.18%  0.2% CobaltOctoate,  0.17%  0.16% 65% in Mineral Spirits Z Corporation 100% zp131 ZCorporation 100% zp102 Z Corporation 100% zp100 Z Corporation 100% zp130Internal Angle 77° ± 3° 52.6° ± 4.9° 36° ± 3° 53° ± 12° 59° ± 13° 32° ±3° 81° ± 9° 48° ± 5° of Friction, 95% Confidence Interval Three Too GoodToo Good Good Too Too Good Dimensional Cohesive Flowable FlowableCohesive Printing suitabilityBased on the results indicated in Table 10, one can conclude thatpowders that have an internal angle of friction greater than 40° andless than 70° are suitable for three dimensional printing in systemsthat use layers on the order of 125 μm.

FIG. 9 a is an exemplary CAD drawing of a test geometry that exhibitsthe distortion caused by the dragging of an article in a powder that istoo flowable. FIGS. 9 b and 9 c are surface finish scans from a VIKINGlaser profilometer from Solarius. The figures show a 3D topographicalrepresentation of articles formed by three dimensional printing. In FIG.9 b, a scan of an article made with zp131 from Z Corporation exhibitssmooth, even contours that closely follow the intended CAD data. FIG. 9c is a scan of a typically “too flowable” powder with an internalfriction angle <40°; the powder is too flowable and unable to resist thespreading forces causing previously printed layers to be displaced,resulting in an article that has a rough and uneven surface finish, oreven has displaced artifacts missing from the surface of the article.The arrow in FIG. 9 c shows where geometry has shifted during printing.

FIG. 10 a is a CAD drawing of the formed article illustrated in FIGS. 10b and 10 c. Referring to FIG. 10 b, as one may expect, a particulatematerial with an internal angle of friction that is between 40° and 70°,e.g., zp131, provides a smoother finish than a particulate material withan internal angle of friction greater than 70° (FIG. 10 c) where thepowder is too cohesive to spread an even layer of particulate material,resulting in an article that has a rough and uneven surface finish.

This test, i.e., determination of an internal angle of friction, is auseful technique for identifying relative performance properties betweendifferent candidate materials. The preferred method for evaluating flowproperties of candidate build materials during formal optimization afterinitial selection is to test samples of the material on a workingthree-dimensional printer. Certain pathological geometries are known tothose experienced in the art, and they can be evaluated eitherqualitatively or quantitatively. One particularly useful article forobserving stability during spreading is a flat plate studded with pegsthat are oriented downward during the build. During printing, theearliest layers addressed are a series of disconnected patches that arerelatively free to shift in the build material. After these have beenformed, a plate is printed that joins all of the pegs together in asingle object. One can easily examine whether the pegs are uniform andstraight, and one can evaluate the quality of spreading on that basis.

Those skilled in the art will readily appreciate that all parameterslisted herein are meant to be exemplary and actual parameters dependupon the specific application for which the methods and materials of thepresent invention are used. It is, therefore, to be understood that theforegoing embodiments are presented by way of example only and that,within the scope of the appended claims and equivalents thereto, theinvention may be practiced otherwise than as specifically described.

1-18. (canceled)
 19. A method for forming an article by threedimensional printing, the method comprising the steps of: providing aparticulate material comprising a plurality of adjacent particles, theparticulate material comprising an aqueous-insoluble thermoplastic;applying to at least some of the plurality of particles an aqueous fluidbinder in an amount sufficient to bond those particles together todefine the article; and immersing the article in a liquid infiltrantmedium.
 20. The method of claim 19, wherein the liquid infiltrant mediumcomprises a hydroxylated hydrocarbon.
 21. The method of claim 20,wherein the liquid infiltrant medium further comprises a plasticizer.22. The method of claim 19, wherein the particulate material furthercomprises at least one of plaster, a water-soluble adhesive, a retarder,an accelerator, and a processing aid. 23-27. (canceled)
 28. The methodof claim 19, wherein the liquid infiltrant medium comprises 0-99.99% byweight hydroxylated hydrocarbon, 0-99.99% by weight a solid wax,0-99.99% by weight a plasticizer, and 0.01-5% by weight a stabilizer.29. The method of claim 28, wherein the hydroxylated hydrocarboncomprises a hydrocarbon diol with a molecular weight greater than 118g/mol, a melting point greater than 30° C., and a kinematic viscosity ofless than or equal to 150 centiStokes at a temperature of at least 50°C.
 30. The method of claim 29, wherein the hydrocarbon diol comprisesoctane diol.
 31. The method of claim 29, wherein the hydrocarbon diolcomprises decane diol.
 32. The method of claim 28 wherein the liquidinfiltrant medium comprises 69.99-99.99% by weight hydroxylatedhydrocarbon, 0-30% by weight a plasticizer, and 0.01-5% by weight astabilizer.
 33. The method of claim 28 wherein the liquid infiltrantmedium comprises 79.99-99.99% by weight solid wax, 0-20% by weight aplasticizer, and 0.01-5% by weight a stabilizer.
 34. The method of claim28, wherein the hydroxylated hydrocarbon comprises an alcohol having aboiling point selected from a range of 25° C. to 100° C., and theplasticizer has a boiling point selected from a range of 25° C. to 100°C.
 35. The method of claim 34, wherein the alcohol comprisesisopropanol.
 36. The method of claim 34, wherein the plasticizercomprises ethanol.
 37. The method of claim 19 wherein the liquidinfiltrant medium comprises 30-100% by weight fugitive hydroxylatedhydrocarbon, 0-50% by weight a solvent, and 0-30% by weight aplasticizer.
 38. The method of claim 19, wherein the particulatematerial comprises (i) an aqueous-insoluble thermoplastic particulatematerial selected from the group consisting of a polyamide 6-3 andtherphthalic acid copolymer, cyclic polyolefins, and combinationsthereof, (ii) plaster, and (iii) a water-soluble adhesive.
 39. Themethod of claim 19, wherein the liquid infiltrant medium compriseshydroxylated hydrocarbon including (i) a hydrocarbon diol with amolecular weight greater than 118 g/mol and a melting point greater than30° C. and (ii) a plasticizer.
 40. The method of claim 39, wherein thehydroxylated hydrocarbon comprises decane diol.
 41. The method of claim39, wherein the plasticizer comprises benzene sulfonamide.
 42. Themethod of claim 39, wherein the plasticizer comprises propylenecarbonate.